Spatiotemporal characterization of interfacial Faraday waves by means of a light absorption technique

We present measurements of the complete spatiotemporal Fourier spectrum of Faraday waves. The Faraday waves are generated at the interface of two immiscible index matched liquids of different density. By use of a light absorption technique we are able to determine the bifurcation scenario from the flat surface to the patterned state for each complex spatial and temporal Fourier component separately. The surface spectra at onset are found to be in good agreement with the predictions from the linear stability analysis. For the nonlinear state our measurements show in a direct manner how energy is transferred from lower to higher harmonics and we quantify the nonlinear coupling coefficients. Furthermore we find that the nonlinear coupling generates static components in the temporal Fourier spectrum leading thus to a contribution of a nonoscillating permanent sinusoidal deformed surface state. A comparison of hexagonal and rectangular patterns reveals that spatial resonance can give rise to a spectrum that violates the temporal resonance conditions given by the weakly nonlinear theory.